Riemann-Hilbert problems and N-soliton solutions for a coupled mKdV system

A 3 × 3 matrix spectral problem is introduced and its associated AKNS integrable hierarchy with four components is generated. From this spectral problem, a kind of Riemann-Hilbert problems is formulated for a system of coupled mKdV equations in the resulting AKNS integrable hierarchy. N-soliton solutions to the coupled mKdV system are presented through a specific Riemann-Hilbert problem with an identity jump matrix.